Six-meson amplitude in QCD-like theories

Abstract

We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudoreal representations, i.e. with global symmetry and breaking patterns $\mathrm{SU}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(n)/\mathrm{SU}(n)$ (extending the QCD case), $\mathrm{SU}(2n)/\mathrm{SO}(2n)$, and $\mathrm{SU}(2n)/\mathrm{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of ten six-meson subamplitudes based on the flavor and group structures. We extend on our previous results obtained within the framework of the $\mathrm{O}(N+1)/\mathrm{O}(N)$ nonlinear sigma model, with $N$ being the number of meson flavors. This work allows for studying a number of properties of six-particle amplitudes at one-loop level.